Additive rank-one nonincreasing maps on Hermitian matrices over the field GF(2[sup]2)
A complete classification of additive rank-one nonincreasing maps on hermitian matrices over Galois field ▫$GF(2^2)$▫ is obtained. This field is special and was not covered in a previous paper. As a consequence, some known applications, like the classification of additive rank-additivity preserving maps, are extended to arbitrary fields. An application concerning the preservers of hermitian varieties is also presented.
Klasificirane so vse aditivne preslikave, ki ne povečujejo ranga ena na hermitskih matrikah s koeficienti iz obsega ▫$GF(2^2)$▫. Ta obseg je poseben in ni bil obravnavan v predhodnem članku. Nekatere znane aplikacije, kot je klasifikacija vseh aditivnih preslikav, ki ohranjajo aditivnost ranga, so posplošene na poljuben komutativen obseg. Klasificirane so tudi vse aditivne preslikave, ki ohranjajo kardinalnost hermitskih varietet.
2009
2016-04-08 16:46:43
1033
mathematics, linear algebra, additive preserver, hermitian matrices, rank, Galois field, weak homomorphism of a graph
matematika, linearna algebra, aditivni ohranjevalci, hermitske matrike, rang, Galoisevi obsegi, šibki homomorfizmi grafov
r6
Marko
Orel
70
Bojan
Kuzma
70
ISSN
2
1081-3810
UDK
4
512.643
OceCobissID
13
13706329
COBISS.SI-ID
3
15240793
0
Predstavitvena datoteka
2016-04-08 16:46:43
vol18_pp482-499.pdf
263533
Predstavitvena datoteka
2018-03-15 18:57:42